Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 76

where S , W/m 2 , is the solar radiosity at the Earth's surface, τ d is the transmissivity of
deck, and ε f =

1 is the floor emissivity.
Energy exchanged by radiation between deck and chimney:

ε d ϕ d - ch π

4 [ D f

( c D D 2 ) 2 ] σ ( T d , eff − T ch ) E d - ch = − (c)

where σ is the Boltzmann constant for black radiation, T d , eff is the effective temperature
of the deck, and c D is the factor to account on thickness of the chimney wall. The view
factor ϕ d - ch can be calculated from reciprocity relation:
ϕ d - ch π

4 [ D f

( c D D 2 ) 2 ] − = ϕ ch - d πc D D 2 ( H 3 − H 2 ) (d)

It can be derived that ϕ ch - d = 0 . 5 · (90 − β ) / 90 where the angle β is determined by

tan β = H 3 /D f .

Energy exchanged by radiation between floor and deck:

2 ·

A d σ ( T f , eff − T d , eff ) E f - d = (e)

= ·

where T f , eff is the effective temperature of the floor and surface area A d π

( D f − D 1 ) / 4.

The following formulae are applied for convection heat transfer from:

floor to air:

E f - a = A d k f - a ( T f , eff − T a , eff ) (f)

deck to air:

E d - a = A d k d - a ( T d , eff − T a , eff ) (g)

deck to environment:

E d -0 = A d k d -0 ( T d , eff − T 0 ) (h)

chimney to environment:

E ch -0 = A ch k ch -0 ( T ch − T 0 ) (i)

and chimney air to chimney wall:

H 2 ) k a - ch T a ,2 T ch

+

T a ,3

= − −

E a - ch πD 2 ( H 3 (j)

2

where k is the respective coefficient and the chimney surface A ch = π · c D · D 2 · ( H 3 −

H 2 ). It is assumed that the coefficient k a - ch = Nu · λ/D 2 where λ = 0 . 0267 W/(m K)

Re 0 . 8 Pr 0 . 4 is thermal conductivity of air and the Nusselt number Nu = 0 . 023 · · and

where the Prandtl number for air is Pr = 0 . 7 and the Reynolds number Re = w 2 · D 2 /ν ,

10 − 5 m 2 /s).

(kinematic viscosity coefficient for air ν = 1 . 6 ·